I find that its easier to avoid hitting adjacent strings when playing on the G and E strings, because the hand has more room to maneuver.
Also, playing at higher positions depresses the strings significantly. Since that is the case, it makes playing higher positions on the D and A strings frustrating, because you easily ends up playing chords instead of single notes.
Is there preference for playing high positions on G and E? (and, but not to distract from the main question) chords on the D and A strings?